The Turing Dimension

If tragedy, or a certain philosophical interpretation of tragedy, is the origin and matrix of speculative thought in general, and dialectical thought in particular, the emerging phenomena that is about to explode into the virtual universe of possible worlds will not escape the resonance of the tragic effect that accompanies and haunts speculative endeavors. The philosophical impulse behind tragedy, according to Philippe Lacoue-Labarthe, is a dialectic of tones that schematizes the opposition of the ideal tone (the subjective aspiration toward the absolute) and the heroic artistic tone of discord or agon in order to arrive at a higher unity or resolution in the One-All through the spirit of the poetic genre. The poetic genre, in the current situation, is about to become the only genre that is based on an algorithmic conception of the world where everything enters into an extended wandering under the unthinkable while being sustained by the elusive umbrella of the intractable. It would eventually unfold itself into a drama of appearances and disappearances implicated within a virtual labyrinth that is, properly speaking, the work of the infinite itself. For those who are eager to achieve communion, the virtual membrane of space would be more than adequate since it provides an immersive arena within which such a fusion can take hold of and thereby permeate into the imaginary, albeit ecstatic, soul of the subject. Whereas for those who remain in tension toward that which cannot be encapsulated or embodied, the green membrane of space is merely a global cockpit that is directed toward the absolute infinite beyond the threshold of representation. Nonetheless, the emerging drama signifies the coming of age of the Pythagorean premonition of the world as numbers, and the permutation of numbers in the form of bits would provide the new materiality necessary for a cosmopolitical drama to stage itself on the new plane of immanence destined to rise to the level of an epic proportion.

Seen form this light, the recurrence of tragedy has been in the making for the last two thousand years beginning with Euclidís axiomatic treatment of geometry, Leibnizís quest for a symbolic logic, and Russellís and Whiteheadís monumental Principia Mathematica in the early part of the twentieth century. It is a consequence of the manifest destiny of instrumental reason whose aim, on the one hand, is to verify and control knowledge by means of a mechanization of mathematics that finds concrete expression in the Universal Turing Machine (UTM), and on the other, to enter into a communion with the substance of affects engendered by the instrumental use of reason. The tragic effect is a dialectic of fusion, of numbers and beings driven by a utopic impulse into an epic dramatology of transubstantiation.

In this echo of tragedy, the subject is mediated by the Universal Turing Machine, which will, in due time, prove to be a gnostic medium that operates on the logic of functional synthesis. It is a machinic alchemy of subjectivation that enfolds both the subject and the object of architecture into the instrumental medium by generating a universal surface upon which a mutant reality can exfoliate into a possible world. This tragic dimension is the scene of a transfusion where the Subject of speculative Idealism finds him/herself immersed into the manifold cockpit of the topological surface now being engendered by the Universal Turing Machine. It is a trajectory that becomes infused with the medium by steering from within the infinite movements of thought and lines of flight in order to overcome, through a dialectics of transgression, the fabric of mimetology brought on by the machine of the double bind. It is at once a catharsis of the subject and of the medium that represents both the substance of Aristotelian mimesis as a mode of poiesis and mimesis in the sense of mimetism or imitation. It is this aspiration for overcoming through sublimation that turns into a play of mourning, which lies behind every metaphysical desire, that induces a philosophy of the tragic effect, or tragic pleasure of the sublime, by situating the subject of architecture in an in-between space of melancholy, or, to use Platoís designation, metaxy. Even though it is at once the nearest and yet the farthest from absolute fulfillment, it may require the intrusion of the caesura so that what appears is not the alternation of representations or simulations but the limits of representation itself.

With the publication of the paper On Computable Numbers, with an Application to the Entscheidungsproblem in 1936, Alan Turing launched the specification for an abstract machine that would ultimately engender a new world by laying out a new plane of immanence specific to its mode of formal implementation. This plane is the virtual arena upon which diagrammatic flows and constructions are instantiated by the abstract machine. The birth of the Universal Turing Machine (UTM) marks the inauguration of the Infozoic Era (the artificial life of self-organizing information systems) by redefining the projective content of the plane of immanence as information-theoretic in origin. It is the harbinger of a new breed of biomechanical species and carries with it the germ of a brave new world more fantastic and hyperbolic than anything we have seen in the history of human civilization. In its most significant form, the UTM is not merely another instrument in the history of technical inventions; it is a computational monad that redefines a new plane of immanence as the spectacle of a second order nature transposed onto the cultural universe of humanity that is founded upon the first order nature. As a generative mechanism, the UTM has brought to the foreground a universe of counterfactual possibilities by showing that these potential states of affairs are inextricably woven into the invisible fabric of reality itself. Its latent ambition is to exfoliate this reality in all its manifestations through the inner workings of the Turing Dimension that is the very heart and soul of the Universal Turing Machine.

The UTM is a logical counterpart of Leibnizís idea of the metaphysical monad. In its most esoteric form, the Universal Turing Machine (UTM) is a computational monad that, through sequential iterations of bits, perpetually induces an internal model, or perception (Leibnizís term for the same feature within a monad), of the world by means of an internal principle that continually modifies its internal state to arrive at a more comprehensive version of the model or perception of the world. It is a machinic idea of a perpetual computing system, or an abstract evolutionary machine, latent with the capacity to self-organize and transforms itself, at least in principle, into possible states of a monad without end. In other words, the UTM is a primitive precursor of a biomechanical species with the metaphysical ambition to embody a machinic form of artificial life and neural intelligence. Since the UTM is the simplest and the most general type of computing system, its internal principle or program could be made to accommodate a generalized form of genetic algorithm. It could, in principle, evolve through self-replication and mutation into ever more complex states of monadic encoding by incorporating new axioms into its existing matrix of axioms. In the process, it would bifurcate into other self-replicating UTMís, each of which in turn would bifurcate and nest other self-replicating UTMís to form an epigenetic landscape of computational monads or a machinic phylum comprised of Universal Turing Machines. Even though the Leibnizian monad continually engages in simultaneous, albeit non-linear, modification of multiplicities as it develops into higher levels of complexity, the UTM is a one-dimensional cellular automata that self-organizes and transforms itself by incessantly rewriting the binary digits registered on the tape that constitutes the Turing Dimension. It is a one-dimensional universe of monadic states generated by the perpetually evolving code of the machine.

The Turing Dimension, together with the arrow of time, establishes the plane of reference necessary for the mapping and projection of the Turing Surface into the plane of expression. The assemblage of interconnected weavings of diverse Turing Surfaces form a Universal Turing Surface engendered by the machininc phylum of Universal Turing Machines. The Surface oscillates according to the dynamic flow of information outputted by each scanning particle as it scans and rewrites bits along the linear sequence of cells marked on the tape of the Turing Dimension of each machine. The scanning particle zigzags through one domain of well-ordered sequence of bits to another by passing through non-well-defined sequence of bits (random sequence) and by overcoming halting programs in order to gradually regain another sequence of well-ordered state of the monad. Such a perpetual Turing Machine is an abstract machine made to sustain by modifying itself within the intertextual context of other Universal Turing Machines. Each Turing Dimension therefore is an aperiodic time machine that weaves a fractal surface with inflections and perturbations that amplify to form holes and vortices on the Universal Turing Surface. These are the caesurae of the Turing Dimension that interrupt the crazed oscillations of the tragic effect induced by the dialectics of functional synthesis operating in complicity with the Universal Turing Machine.

In the brave new world that has begun to unfold, the horizons of the tragic effect will no doubt resonate on the virtual contours of the Universal Turing Surface that is currently expanding into potential space. The Universal Turing Surface is an active matrix or cellular automata percolating and filtering out the universe of potential events into virtual events and cross-pollinating these virtual circuits by registering them on the plane of immanence as the actualized web of diagrammatic flows and singularities. Every plane of immanence is a cross section of the configuration space of a possible world. It is a finite incarnation of the potential infinite that is severely constrained and channeled through linear iterations of the Universal Turing Machine. The UTM therefore is a diagrammatic machine that rolls and unrolls the Universal Turing Surface into architectures of the manifold cockpit that navigates by incessantly opening up a universe of possible world. The ambition of the Universal Turing Machine is to encapsulate Leibnizís notion of the Principle of Sufficient Reason by rising to the level expressive of an oracle and thereby disclosing the hidden voice of reality on the inner Surface of the Turing Machine. This voice, the obscure sirens of the muses from beyond, or, simply, the words within the voice, would be a script in the form of a binary string or an interger that exfoliate the Turing Dimension into the fabric of the Universal Turing Surface as the Surface of the One-All. It is mimesis in the most intrinsic sense in that it appeals to a formal representation of the universe as a pre-established harmony of coordinated monads that form a plenum.

Herein lies the supreme irony of a gnostic quest that may well be usurped by the very instrument that promises to deliver. The internal principle and the internal complexity contained within each computational monad is dependent on the universe of computable functions drawn from the universe of mathematics that has proven to be irreducibly random and incomplete. As a consequence, any algorithmic compression that reflects the matrix of the internal complexity would be a code that is irreducibly random, a specific kind of randomness that is qualitatively different from any random scrambling of bits. By extension, any attempt at a compression of a theory of everything that embodies the Principle of Sufficient Reason cannot be reduced to a Principle of Maximal Compression, or Metacode, without containing large amounts of random information that, in principle, cannot be compressed. According to Algorithmic Information Theory as developed by Gregory Chaitin, it would not be possible to prove that the Metacode in question is the absolute minimal string that outputs a maximum of possible effects. If the world is the infinite effect of an infinite cause, there are, in all likelihood, no binary strings that can encapsulate the hidden logic of the infinite cause in its entirety. The drama of the incomplete thus haunts the infinite extensibility of the tragic effect induced by the Turing Dimension, which, in turn, maps and haunts the infinite expanse of the Universal Turing Surface ingrained with holes and vortices amidst an infozoic (self-organizing systems) ecology teeming with artificial life forms. These holes and vortices are interruptions or caesurae due to intractable problems derived from the incompleteness and undecidability of certain propositions concerning the logic and limits of computation. Let it suffice for the moment to say that, the Turing Dimension is the potential infinite interspersed with breaks or interruptions that lie between overlapping dimensions of the tragic effect. The Universal Turing Surface is the instrumental medium that exfoliates into a topo-dramatology of the virtual cockpit of architecture infused with an ambivalent mixture of exultation and despair. It is a theatre where the very excess of the speculative switches into the very excess of submission to finitude (Lacoue-labarthe), as defined, in this context, by the logic of computability. It is at once a tragic comedy and a machinic philosophy of the tragic effect. Nothing symbolizes the emergence of the Infozoic Era more clearly and explicitly than the emergence of the Universal Turing Surface that lays out a virtual cartography of a possible world among an infinite number of possible worlds. Architecture is implicated in the folds of this cartography that has become the green membrane of space suspended in a twilight zone that is everywhere and nowhere. The Universal Turing Surface is the phase space topology engendered by the cyclothmic oscillations of the Universal Turing Machine. The Surface is nonetheless permeated with the Caesura of the Turing Dimension, which allows each interruption to sustain a pause or the empty moment, the absence of moment that, if luck is with it, may allow for the intrusion of the prophetic word. The Universal Turing Surface is the new plane of immanence that is, above all else, a cosmopolitical orchestration, an onto-organology that constitutes by organizing itself into a self-synthesized organ of a self-synthesized information system within demiurgic space. .

© Karl S. Chu / X Kavya Los Angeles, 1999